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Abstract:

We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients bp that in particular verify that limp→∞ bp = b uniformly in Ω¯, we prove that there is a uniform limit of upj (along a sequence pj →∞) and that this limit is a Kantorovich potential for the optimal mass transport problem of f+ to f- with cost c(x, y) given by the formulac(x, y) = infσ(0)=x,σ(1)=y fσbds.

Registro:

Documento: Artículo
Título:Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, Alicante, 03080, Spain
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:Mass transport; Monge-Kantorovich problems; P-Laplacian equation
Año:2014
Volumen:3
Número:3
Página de inicio:133
Página de fin:140
DOI: http://dx.doi.org/10.1515/anona-2013-0022
Título revista:Advances in Nonlinear Analysis
Título revista abreviado:Adv. Nonlinear Anal.
ISSN:21919496
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21919496_v3_n3_p133_Mazon

Referencias:

  • Ambrosio, L., Lecture notes on optimal transport problems (2003) Mathematical Aspects of Evolving Interfaces (Funchal 2000), Lecture Notes in Math., 1812, pp. 1-52. , Springer-Verlag, Berlin
  • Ambrosio, L., Pratelli, A., Existence and stability results in the L1 theory of optimal transportation (2003) Optimal Transportation and Applications (Martina Franca 2001), Lecture Notes in Math., 1813, pp. 123-160. , Springer-Verlag, Berlin
  • Bhattacharya, T., Di Benedetto, E., Manfredi, J., Limits as p → ∞ of δ<inf>p</inf>u<inf>p</inf> = f and related extremal problems (1991) Rend. Semin. Mat. Univ. Politec. Torino, pp. 15-68
  • Evans, L.C., Partial differential equations and monge-kantorovich mass transfer (1999) Current Developments in Mathematics 1997, pp. 65-126. , (Cambridge 1997), International Press, Boston
  • Evans, L.C., Gangbo, W., Differential equations methods for the monge-kantorovich mass transfer problem (1999) Mem. Amer. Math. Soc., 137 (653)
  • Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J., A monge-kantorovich mass transport problem for a discrete distance (2011) J. Funct. Anal., 260, pp. 3494-3534
  • López-Soriano, R., Navarro-Climent, J.C., Rossi, J.D., The infinity laplacian with a transport term (2013) J. Math. Anal. Appl., 398, pp. 752-765
  • Mazón, J.M., Rossi, J.D., Toledo, J., An optimal matching problem for the euclidean distance (2014) SIAM J. Math. Anal., 46 (1), pp. 233-255
  • Mazón, J.M., Rossi, J.D., Toledo, J., An optimal transportation problem with a cost given by the euclidean distance plus import/export taxes on the boundary (2014) Rev. Mat. Iberoam., 30 (1), pp. 277-308
  • Mazón, J.M., Rossi, J.D., Toledo, J., Mass transport problems for the euclidean distance obtained as limits of p-laplacian type problems with obstacles (2014) J. Differential Equations, 256 (9), pp. 3208-3244
  • Villani, C., Topics in optimal transportation (2003) Grad. Stud. Math., 58. , American Mathematical Society, Providence
  • Villani, C., Optimal transport. Old and new (2009) Grundlehren Math. Wiss., 338. , Springer-Verlag, Berlin

Citas:

---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2014) . Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence. Advances in Nonlinear Analysis, 3(3), 133-140.
http://dx.doi.org/10.1515/anona-2013-0022
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence" . Advances in Nonlinear Analysis 3, no. 3 (2014) : 133-140.
http://dx.doi.org/10.1515/anona-2013-0022
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence" . Advances in Nonlinear Analysis, vol. 3, no. 3, 2014, pp. 133-140.
http://dx.doi.org/10.1515/anona-2013-0022
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence. Adv. Nonlinear Anal. 2014;3(3):133-140.
http://dx.doi.org/10.1515/anona-2013-0022